(3w+2)(3w-2)=-w^2+26w-16

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Solution for (3w+2)(3w-2)=-w^2+26w-16 equation: 


Simplifying
(3w + 2)(3w + -2) = -1w2 + 26w + -16

Reorder the terms:
(2 + 3w)(3w + -2) = -1w2 + 26w + -16

Reorder the terms:
(2 + 3w)(-2 + 3w) = -1w2 + 26w + -16

Multiply (2 + 3w) * (-2 + 3w)
(2(-2 + 3w) + 3w * (-2 + 3w)) = -1w2 + 26w + -16
((-2 * 2 + 3w * 2) + 3w * (-2 + 3w)) = -1w2 + 26w + -16
((-4 + 6w) + 3w * (-2 + 3w)) = -1w2 + 26w + -16
(-4 + 6w + (-2 * 3w + 3w * 3w)) = -1w2 + 26w + -16
(-4 + 6w + (-6w + 9w2)) = -1w2 + 26w + -16

Combine like terms: 6w + -6w = 0
(-4 + 0 + 9w2) = -1w2 + 26w + -16
(-4 + 9w2) = -1w2 + 26w + -16

Reorder the terms:
-4 + 9w2 = -16 + 26w + -1w2

Solving
-4 + 9w2 = -16 + 26w + -1w2

Solving for variable 'w'.

Reorder the terms:
-4 + 16 + -26w + 9w2 + w2 = -16 + 26w + -1w2 + 16 + -26w + w2

Combine like terms: -4 + 16 = 12
12 + -26w + 9w2 + w2 = -16 + 26w + -1w2 + 16 + -26w + w2

Combine like terms: 9w2 + w2 = 10w2
12 + -26w + 10w2 = -16 + 26w + -1w2 + 16 + -26w + w2

Reorder the terms:
12 + -26w + 10w2 = -16 + 16 + 26w + -26w + -1w2 + w2

Combine like terms: -16 + 16 = 0
12 + -26w + 10w2 = 0 + 26w + -26w + -1w2 + w2
12 + -26w + 10w2 = 26w + -26w + -1w2 + w2

Combine like terms: 26w + -26w = 0
12 + -26w + 10w2 = 0 + -1w2 + w2
12 + -26w + 10w2 = -1w2 + w2

Combine like terms: -1w2 + w2 = 0
12 + -26w + 10w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -13w + 5w2) = 0

Factor a trinomial.
2((3 + -5w)(2 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -5w)' equal to zero and attempt to solve:

Simplifying
3 + -5w = 0

Solving
3 + -5w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -5w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5w = 0 + -3
-5w = 0 + -3

Combine like terms: 0 + -3 = -3
-5w = -3

Divide each side by '-5'.
w = 0.6

Simplifying
w = 0.6

Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {0.6, 2}

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